Rigging a Pac-Man-like character
I just made an example.




Bind each half loop to each control bone;
Add a bone constraint called Copy Rotation to each bone except the outermost one, set all target as the outmost bone (the longest one in the image below), adjust the Influence value for each degressively.
After that, you can control the open/close action simply by just tweaking the outermost bone.